EP3264611A1 - Qc-ldpc coding methods and apparatus - Google Patents

Abstract

Concepts and schemes pertaining to quasi-cyclic-low-density parity-check (QC-LDPC) coding are described. A processor of an apparatus may generate a QC-LDPC code having a plurality of codebooks embedded therein. The processor may select a codebook from the plurality of codebooks. The processor may also encode data using the selected codebook. Alternatively or additionally, the processor may generate the QC-LDPC code including at least one quasi-row orthogonal layer. Alternatively or additionally, the processor may generate the QC-LDPC code including a base matrix a portion of which forming a kernel matrix that corresponds to a code rate of at least a threshold value.

Description

CROSS REFERENCE TO RELATED PATENT APPLICATIONS
• The present disclosure claims the priority benefit ofU.S. Provisional Patent Application Ser. No. 62/335,095, filed 12 May 2016,U.S. Provisional Patent Application Ser. No..62/404,236, filed 05 October 2016,U.S. Provisional Patent Application Ser. No. 62/412,337, filed 25 October 2016,U.S. Provisional Patent Application Ser. No. 62/429,915, filed 05 December 2016, andU.S. Provisional Patent Application Ser. No. 62/488,089, filed 21 April 2017. The contents of the aforementioned patent documents are herein incorporated by reference in their entirety.
TECHNICAL FIELD
• The present disclosure is generally related to information coding and decoding and, more particularly, to methods and apparatus of quasi-cyclic-low-density parity-check (QC-LDPC) coding.
BACKGROUND
• Unless otherwise indicated herein, approaches described in this section are not prior art to the claims listed below and are not admitted to be prior art by inclusion in this section.
• The 3^rd Generation Partnership Project (3GPP) has approved plans to speed up the development of the 5^th-generation (5G) New Radio (NR) specifications, it thus can be expected that standards-based 5G NR wireless communications services can be launched in the near future. The 3GPP has also agreed that QC-LDPC will be used for in 5G NR data channel. However, specifics are how QC-LDPC-based coding and decoding are not yet defined.
SUMMARY
• The following summary is illustrative only and is not intended to be limiting in any way. That is, the following summary is provided to introduce concepts, highlights, benefits and advantages of the novel and non-obvious techniques described herein. Select implementations are further described below in the detailed description. Thus, the following summary is not intended to identify essential features of the claimed subject matter, nor is it intended for use in determining the scope of the claimed subject matter.
• An objective of the present disclosure is to propose various novel concepts and schemes pertaining to QC-LDPC coding and decoding, which can be implemented in next-generation communications, whether wired or wireless, including 5G NR wireless communications.
• In one aspect, a method may involve a processor of an apparatus generating a QC-LDPC code having a plurality of codebooks embedded therein. The method may also involve the processor selecting a codebook from the plurality of codebooks. The method may further involve the processor encoding data using the selected codebook.
• In one aspect, a method may involve a processor of an apparatus generating a QC-LDPC code that comprises at least one quasi-row orthogonal layer. The method may also involve the processor encoding data using the QC-LDPC code.
• In one aspect, a method may involve a processor of an apparatus generating a QC-LDPC code that comprises a base matrix a portion of which forming a kernel matrix that corresponds to a code rate of at least a threshold value. The method may also involve the processor encoding data using the QC-LDPC code.
• In one aspect, a method may involve a processor of an apparatus generating a QC-LDPC code. The method may also involve the processor encoding data using the QC-LDPC code. In generating the QC-LDPC code, the method may also involve the processor generating a respective table of shift values for each lifting factor of a first set of lifting factors. The method may further involve the processor optimizing the first set of lifting factors to produce a second set of lifting factors. A number of lifting factors of the first set may be greater than a number of lifting factors of the second set. A first lifting factor that exists in the first set but not in the second set may share a respective table of shift values of a second lifting factor that exists in both the first set and the second set. The second lifting factor may be smaller than the first lifting factor in value and closest to the first lifting factor than other lifting factors in the first set.
• It is noteworthy that, although description of the proposed scheme and various examples is provided below in the context of 5G NR wireless communications, the proposed concepts, schemes and any variation(s)/derivative(s) thereof may be implemented in communications in accordance with other protocols, standards and specifications where implementation is suitable. Thus, the scope of the proposed scheme is not limited to the description provided herein.
BRIEF DESCRIPTION OF THE DRAWINGS
• The accompanying drawings are included to provide a further understanding of the disclosure, and are incorporated in and constitute a part of the present disclosure. The drawings illustrate implementations of the disclosure and, together with the description, serve to explain the principles of the disclosure. It is appreciable that the drawings are not necessarily in scale as some components may be shown to be out of proportion than the size in actual implementation in order to clearly illustrate the concept of the present disclosure.
• FIG. 1 is a diagram of an example multi-embedded LDPC code design in accordance with an implementation of the present disclosure.
• FIG. 2 is a diagram of an example logic flow related to multi-embedded LDPC code design in accordance with an implementation of the present disclosure.
• FIG. 3 is a diagram of an example quasi-row orthogonal layer design in accordance with an implementation of the present disclosure.
• FIG. 4 is a diagram of an example hybrid orthogonality layer design in accordance with an implementation of the present disclosure.
• FIG. 5 is a diagram of an example QC-LDPC code that supports extreme low code rate in accordance with an implementation of the present disclosure.
• FIG. 6 is a diagram of an example kernel matrix design in accordance with an implementation of the present disclosure.
• FIG. 7 is a diagram of an example concept of kernel base matrix in accordance with an implementation of the present disclosure.
• FIG. 8 is a diagram of an example concept of kernel base matrix in accordance with another implementation of the present disclosure.
• FIG. 9 is a diagram of an example shift-coefficient design in accordance with an implementation of the present disclosure.
• FIG. 10 is a block diagram of an example communications system in accordance with an implementation of the present disclosure.
• FIG. 11 is a flowchart of an example process in accordance with an implementation of the present disclosure.
• FIG. 12 is a flowchart of an example process in accordance with another implementation of the present disclosure.
• FIG. 13 is a flowchart of an example process in accordance with another implementation of the present disclosure.
• FIG. 14 is a flowchart of an example process in accordance with another implementation of the present disclosure.
DETAILED DESCRIPTION OF PREFERRED IMPLEMENTATIONS
• Detailed embodiments and implementations of the claimed subject matters are disclosed herein. However, it shall be understood that the disclosed embodiments and implementations are merely illustrative of the claimed subject matters which may be embodied in various forms. The present disclosure may, however, be embodied in many different forms and should not be construed as limited to the exemplary embodiments and implementations set forth herein. Rather, these exemplary embodiments and implementations are provided so that description of the present disclosure is thorough and complete and will fully convey the scope of the present disclosure to those skilled in the art. In the description below, details of well-known features and techniques may be omitted to avoid unnecessarily obscuring the presented embodiments and implementations.
Overview
• The proposed concepts and schemes generally relate to the following areas: multi-embedded LDPC code design, hybrid orthogonal LDPC layer design, QC-LDPC support of extreme low code rate (CR), kernel matrix design, and shift-coefficient design. The area of hybrid orthogonal LDPC layer design includes the novel concepts and schemes of quasi-row orthogonal layer design and hybrid orthogonality layer design. Description of the proposed concepts and schemes is provided below with reference toFIG. 1 - FIG. 9.
• FIG. 1 illustrates an example multi-embedded LDPC code design in accordance with an implementation of the present disclosure. Referring toFIG. 1, a QC-LDPC code 100 in accordance with the present disclosure may have a plurality of codebooks embedded therein.
• As shown inFIG. 1, QC-LDPC code 100 may include a base matrix that includes a parity matrix of a plurality of parity bits and an information matrix of a plurality of information bits. Accordingly, each codebook of the plurality of codebooks may include the parity matrix and a respective portion of the information matrix of a corresponding size such that sizes of the plurality of codebooks are different from one another. In the example shown inFIG. 1, a codebook may be expressed as follows:$$\mathrm{Codebook}=\left(\mathrm{<figure-callout\; label="l"\; filenames="imgf0001.png,imgf0007.png"\; state="\{\{state\}\}">l</figure-callout>}\mathrm{1}\mathrm{or<figure-callout\; label="l"\; filenames="imgf0008.png"\; state="\{\{state\}\}">l</figure-callout>}\mathrm{2}\mathrm{or<figure-callout\; label="l"\; filenames="imgf0008.png"\; state="\{\{state\}\}">l</figure-callout>}\mathrm{3}\right)+\mathrm{P}$$

  
• The notation "I1" represents a first portion of the information matrix, the notation "I2" represents a second portion of the information matrix, the notation "I3" represents a third portion of the information matrix, and the notation "P" represents the parity matrix. Here, a size (e.g., in terms of number of bits and/or memory size) of I1 is greater than a size of I2, which is greater than the size of I3.
• Thus, the size of the resultant codebook may vary, depending on the size of the portion of the information matrix that is utilized in combination with the parity matrix to form the codebook. It is noteworthy that, although the example shown inFIG. 1 depicts three codebooks of different sizes due to the combinations of I1 + P, I2 + P and I3 + P, the number of codebooks of different sizes is not limited to three (and may be fewer or more than three) in various implementations in accordance with the present disclosure.
• In some implementations, each codebook of the plurality of codebooks may correspond to a respective hybrid automatic repeat request (HARQ) threads of a plurality of HARQ threads that are different from one another. For instance, a first codebook may correspond to a first HARQ thread with a value in the range of 0.33 ∼ 0.89. A second codebook may correspond to a second HARQ thread with a value in the range of 0.2 ∼ 0.66. A third codebook may correspond to a third HARQ thread with a small code block size less than 400.
• In some implementations, each codebook of the plurality of codebooks may correspond to a respective memory size (Kb). For instance, a first codebook may correspond to a first memory size Kb = 16. A second codebook may correspond to a second memory size Kb = 12. A third codebook may correspond to a third memory size Kb = 5.
• In some implementations, all codebooks may share one base matrix with different zero-padding sizes. In some implementations, different codebooks may correspond to different shift-coefficient designs or share one shift-coefficient design.
• In some implementations, the selection of which codebook of the multiple codebooks to use may be based on an initial code rate for transmission of the data, a code block size of the data, or both.
• FIG. 2 illustrates anexample logic flow 200 related to multi-embedded LDPC code design in accordance with an implementation of the present disclosure.Logic flow 200 may be implemented in or by an encoder or a processor to effect various features and/or aspects of the proposed concepts and schemes of the present disclosure. More specifically,logic flow 200 ma pertain to selection of a codebook from a number of codebooks.Logic flow 200 may include one or more operations, actions, or functions as represented by one or more ofblocks 210, 220, 230, 240 and 250. Although illustrated as discrete blocks, various blocks oflogic flow 200 may be divided into additional blocks, combined into fewer blocks, or eliminated, depending on the desired implementation.Logic flow 200 may be implemented by each offirst apparatus 1005 andsecond apparatus 1050 described below. Solely for illustrative purposes and without limiting the scope, description oflogic flow 200 is provided below in the context ofsecond apparatus 1050.Logic flow 200 may begin at 210.
• At 210,logic flow 200 may involvesecond apparatus 1050 determining whether a code block size of data to be encoded is less than a threshold code block size. In an event that the code block size of the data is determined to be less than the threshold code block size,logic flow 200 may proceed from 210 to 220. In an event that the code block size of the data is determined to be not less than the threshold code block size,logic flow 200 may proceed from 210 to 230.
• At 220, logic flow may involvesecond apparatus 1050 selecting a first codebook of the plurality of codebooks.
• At 230, logic flow may involvesecond apparatus 1050 determining whether an initial code rate for transmission of the data is greater than a threshold code rate. In an event that the initial code rate is determined to be not greater than the threshold code rate,logic flow 200 may proceed from 230 to 240. In an event that the initial code rate is determined to be greater than the threshold code rate,logic flow 200 may proceed from 230 to 250.
• At 240,logic flow 200 may involvesecond apparatus 1050 selecting a second codebook of the plurality of codebooks.
• At 250,logic flow 200 may involvesecond apparatus 1050 selecting a third codebook of the plurality of codebooks.
• Here, a size of the third codebook is larger than a size of the second codebook. Additionally, the size of the second codebook is larger than a size of the first codebook.
• FIG. 3 illustrates an example quasi-roworthogonal layer design 300 in accordance with an implementation of the present disclosure. Orthogonality is good for LDPC decoder throughput efficiency. In the LDPC code, several rows may be grouped together to form a layer and each column within the layer may be of degree one (i.e., orthogonal). In such cases the layer is referred as a pure row orthogonal layer.
• Referring toFIG. 3, in quasi-roworthogonal layer design 300, several rows may be grouped together to form a quasi-row orthogonal layer. Each column within the layer may be of degree one (i.e., orthogonal) with the exception of one or more punctured columns. In the example shown in part (A) ofFIG 3, the two leftmost columns are punctured columns.
• Moreover, in quasi-roworthogonal layer design 300, there is no cycle within the punctured columns in the quasi-row orthogonal layer. In the example shown in part (B) ofFIG. 3, as a cycle exists within the two punctured columns, the corresponding layer is not considered as a quasi-row orthogonal layer in accordance with the present disclosure.
• FIG. 4 illustrates an example hybridorthogonality layer design 400 in accordance with an implementation of the present disclosure. In hybridorthogonality layer design 400, a QC-LDPC code may include a plurality of portions of different degrees of orthogonality. In the example shown inFIG. 4, blocks of darker color represent bits of 1 while blocks of lighter color represent bits of 0. For instance, a first portion of the plurality of portions may be of a low degree of orthogonality and may correspond to a high code rate. Likewise, a second portion of the plurality of portions may be of a medium degree of orthogonality and may correspond to a medium code rate. Similarly, a third portion of the plurality of portions may be of a high degree of orthogonality and may correspond to a low code rate.
• In the example shown inFIG. 4, the plurality of portions of different degrees of orthogonality include the following: (1) a non-row orthogonal portion including a plurality of rows and a plurality of columns that form at least one non-row orthogonal layer corresponding to relatively higher code rate(s), (2) a quasi-row orthogonal portion including a plurality of rows and a plurality of columns that form the at least one quasi-row orthogonal layer corresponding to medium code rate(s), and (3) a pure-row orthogonal portion including a plurality of rows and a plurality of columns that form at least one pure-row orthogonal layer corresponding to relatively lower code rate(s). Here, each column of the plurality of columns of the non-row orthogonal portion is a column of degree two or more. Additionally, one or more columns of the plurality of columns of the quasi-row orthogonal portion include punctured columns of degree two or more. Moreover, the remaining columns of the plurality of columns of the quasi-row orthogonal portion include non-punctured columns of degree one. Furthermore, each column of the plurality of columns of the pure-row orthogonal portion includes a column of degree one.
• FIG. 5 illustrates an example QC-LDPC code 500 that supports extreme low code rate in accordance with an implementation of the present disclosure. Referring toFIG. 5, QC-LDPC code 500 may include a parity matrix of a plurality of parity bits and an information matrix of a plurality of information bits. The information matrix may include one or more rows of bits each of degree two. Moreover, each bit of bits of the degree two of the one or more rows of bits of degree two may be a previously-used parity bit or a previously-transmitted information bit.
• FIG. 6 illustrates an examplekernel matrix design 600 in accordance with an implementation of the present disclosure. Referring toFIG. 6, inkernel matrix design 600, a QC-LDPC code may include a base matrix with a portion of forming a kernel matrix that corresponds to a code rate of at least a threshold value. For instance, in the example shown inFIG. 6, the kernel matrix supports a code rate of 0.89.
• FIG. 7 illustrates anexample concept 700 of kernel base matrix in accordance with an implementation of the present disclosure. Referring toFIG. 7, the kernel matrix may include a plurality of rows and a plurality of columns of bits, with two or more of the columns being punctured columns having a specific pattern of bits (e.g., one or more bits of 0). In some implementations, the specific pattern of bits in the punctured columns may include an isosceles right triangle of bits of 0, with a right angle of the triangle corresponding to a bit of 0 at an upper-left corner of the punctured columns.
• The kernel matrix may include a parity matrix of a plurality of rows and a plurality of columns of bits. The kernel matrix may also include an information matrix of a plurality of rows and a plurality of columns of bits. The parity matrix may include a matrix having a Wi-Fi pattern (e.g., Wi-Fi like parity matrix). Moreover, more than one rows of bits of the information matrix may include rows of high density of bits of 1 with no or one bit of 0. A bottom row of bits of the plurality of rows may include a first number of bits of 1. The first number may be equal to or greater than a number of punctured columns by 1.
• In the example shown in part (A) ofFIG. 7, the first several rows (e.g., three rows) are composed of Wi-Fi like parity matrix, and the information matrix has very high density of bits of 1. Specifically, each row in the information matrix includes mostly, if not all, bits of 1 with none or one bit of 0. The punctured columns include a specific pattern of one or more bits of 0 after any number of column permutation(s) and/or row permutation(s) (e.g., at least one column permutation, at least one row permutation, or any combination thereof). The bottom row may have three or four edge blocks. One edge block may correspond to parity variable node (VN) block. Two edge blocks may correspond to the two punctured columns (e.g., VN0 and VN1). In cases where there are four edge blocks, the fourth edge block may be added to increaser the minimum distance.
• In the example shown in part (B) ofFIG. 7, an example pattern of the punctured column is shown. For a base matrix of sizem xn and assuming a number ofp columns is/are punctured, am xp matrix may be constructed with an isosceles right triangle of bits of 0, with a right angle of the triangle corresponding to a bit of 0 at an upper-left corner of the punctured columns. Other bits in the punctured column(s) may be randomly selected to be 0 or 1. As row permutation and/or column permutation may be performed, the actual location of the specific pattern may be different from the upper-left corner of the puncture column(s).
• FIG. 8 illustrates anexample concept 800 of kernel base matrix in accordance with another implementation of the present disclosure. Inconcept 800, the kernel matrix includes a Wi-Fi pattern (or Wi-Fi like parity matrix), punctured columns, and remaining portion of the information matrix. The remaining portion of the information matrix may be designed with one of a number of degree distributions. For instance, the kernel matrix may include five rows of bits and twenty columns of bits. A variable node (VN) degree of the twenty columns of bits may include one of the following: [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], and [2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]. A check node (CN) degree of the five rows of bits may include one of the following: [13, 10, 14, 17, 2], [13, 10, 13, 17, 2], [13, 10, 13, 18, 3], [13, 11, 13, 18, 2], [13, 10, 14, 18, 2], [13, 10, 13, 19, 2], [14, 10, 13, 18, 1], [13, 11, 13, 18, 1], [13, 10, 14, 18, 1], [13, 11, 13, 19, 1], [13, 10, 13, 18, 2], and [13, 10, 13, 18, 1].
• FIG. 9 illustrates of an example shift-coefficient design 900 in accordance with an implementation of the present disclosure. For each lifting factor, there may be a table of corresponding shift values. The tables among different lifting factors may be nested designed. In shift-coefficient design 900, a valid set of lifting factors may be defined for use in LDPC encoding. In the example shown inFIG. 9, the valid set of lifting factors includes the following lifting factors of different values: Z = 16, Z = 24, Z = 32, Z = 48, Z = 64, Z = 96, Z = 128, Z = 192, Z = 256 and Z = 384. In shift-coefficient design 900, the valid set of lifting factors may be optimized to obtain an optimized set of lifting factors. The number of lifting factors in the optimized set is less than the number of lifting factors in the valid set. The table of shift values designed for the closest and smaller or equal lifting factor within the optimized set may be used. For instance, the table of shift values designed for the lifting factor Z = 32 may be shared by the lifting factor Z = 48. Similarly, the table of shift values designed for the lifting factor Z = 128 may be shared by the lifting factor Z = 192.
Illustrative Implementations
• FIG. 10 illustrates anexample communications system 1000 in accordance with an implementation of the present disclosure. Communications systems may include afirst apparatus 1005 and asecond apparatus 1050, which may be in communications with each other via acommunications link 1040. Each offirst apparatus 1005 andsecond apparatus 1050 may perform various functions as a communication device to implement concepts, schemes, techniques, processes and methods described herein pertaining to QC-LDPC coding, including those described with respect to some or all ofFIG. 1 - FIG. 9 as well asprocesses 1100, 1200 and 1300 described below. More specifically, each offirst apparatus 1005 andsecond apparatus 1050 may implement various aspects of the proposed concepts and schemes pertaining to multi-embedded LDPC code design, hybrid orthogonal LDPC layer design, QC-LDPC support of extreme low code rate, kernel matrix design, and shift-coefficient design.
• Each offirst apparatus 1005 andsecond apparatus 1050 may be a part of an electronic apparatus which may be a communication device, a computing apparatus, a portable or mobile apparatus, or a wearable apparatus. For instance,first apparatus 1005 may be implemented in a Wi-Fi access point, a smartphone, a smartwatch, a smart bracelet, a smart necklace, a personal digital assistant, or a computing device such as a tablet computer, a laptop computer, a notebook computer, a desktop computer, or a server. Likewise,second apparatus 1050 may be implemented in a Wi-Fi mobile client or station, a smartphone, a smartwatch, a smart bracelet, a smart necklace, a personal digital assistant, or a computing device such as a tablet computer, a laptop computer, a notebook computer, a desktop computer, or a server. Alternatively, each offirst apparatus 1005 andsecond apparatus 1050 may be implemented in the form of one or more integrated-circuit (IC) chips such as, for example and not limited to, one or more single-core processors, one or more multi-core processors, or one or more complex-instruction-set-computing (CISC) processors.
• Each offirst apparatus 1005 andsecond apparatus 1050 may include at least some of those components shown inFIG. 10, respectively. For instance,first apparatus 1005 may include at least aprocessor 1010, andsecond apparatus 1050 may include at least aprocessor 1060. Additionally,first apparatus 1005 may include amemory 1020 and/or atransceiver 1030 configured to transmit and receive data wirelessly (e.g., in compliance with one or more 3GPP stands, protocols, specifications and/or any applicable wireless protocols and standards). Each ofmemory 1020 andtransceiver 1030 may be communicatively and operably coupled toprocessor 1010. Similarly,second apparatus 1050 may also include amemory 1070 and/or atransceiver 1080 configured to transmit and receive data wirelessly (e.g., in compliance with the IEEE 802.11 specification and/or any applicable wireless protocols and standards). Each ofmemory 1070 andtransceiver 1080 may be communicatively and operably coupled toprocessor 1060. Each offirst apparatus 1005 andsecond apparatus 1050 may further include other components (e.g., power system, display device and user interface device), which are not pertinent to the proposed scheme of the present disclosure and, thus, are neither shown inFIG. 10 nor described herein in the interest of simplicity and brevity.
• Transceiver 1030 may be configured to communicate wirelessly in a single frequency band or multiple frequency bands.Transceiver 1030 may include atransmitter 1032 capable of transmitting data wirelessly and areceiver 1034 capable of receiving data wirelessly. Likewise,transceiver 1080 may be configured to communicate wirelessly in a single frequency band or multiple frequency bands.Transceiver 1080 may include atransmitter 1082 capable of transmitting data wirelessly and areceiver 1084 capable of receiving data wirelessly.
• Each ofmemory 1020 andmemory 1070 may be a storage device configured to store one or more sets of codes, programs and/or instructions and/or data therein. In the example shown inFIG. 10,memory 1020 stores one or more sets of processor-executable instructions 1022 anddata 1024 therein, andmemory 1070 stores one or more sets of processor-executable instructions 1072 anddata 1074 therein. Each ofmemory 1020 andmemory 1070 may be implemented by any suitable technology and may include volatile memory and/or non-volatile memory. For example, each ofmemory 1020 andmemory 1070 may include a type of random access memory (RAM) such as dynamic RAM (DRAM), static RAM (SRAM), thyristor RAM (T-RAM) and/or zero-capacitor RAM (Z-RAM). Alternatively or additionally, memory 520 may include a type of read-only memory (ROM) such as mask ROM, programmable ROM (PROM), erasable programmable ROM (EPROM) and/or electrically erasable programmable ROM (EEPROM). Alternatively or additionally, each ofmemory 1020 andmemory 1070 may include a type of non-volatile random-access memory (NVRAM) such as flash memory, solid-state memory, ferroelectric RAM (FeRAM), magnetoresistive RAM (MRAM) and/or phase-change memory.
• In one aspect, each ofprocessor 1010 andprocessor 1060 may be implemented in the form of one or more single-core processors, one or more multi-core processors, or one or more CISC processors. That is, even though a singular term "a processor" is used herein to refer to each ofprocessor 1010 andprocessor 1060, each ofprocessor 1010 andprocessor 1060 may include multiple processors in some implementations and a single processor in other implementations in accordance with the present disclosure. In another aspect, each ofprocessor 1010 andprocessor 1060 may be implemented in the form of hardware (and, optionally, firmware) with electronic components including, for example and without limitation, one or more transistors, one or more diodes, one or more capacitors, one or more resistors, one or more inductors, one or more memristors and/or one or more varactors that are configured and arranged to achieve specific purposes in accordance with the present disclosure. In other words, in at least some implementations, each ofprocessor 1010 andprocessor 1060 is a special-purpose machine specifically designed, arranged and configured to perform specific tasks including QC-LDPC coding in accordance with various implementations of the present disclosure.
• Processor 1010, as a special-purpose machine, may include non-generic and specially-designed hardware circuits that are designed, arranged and configured to perform specific tasks pertaining to QC-LDPC coding in accordance with various implementations of the present disclosure. In one aspect,processor 1010 may execute the one or more sets of codes, programs and/orinstructions 1022 stored inmemory 1020 to perform various operations to render QC-LDPC coding in accordance with various implementations of the present disclosure. In another aspect,processor 1010 may include anencoder 1012 and adecoder 1014 that, together, perform specific tasks and functions to render QC-LDPC coding in accordance with various implementations of the present disclosure. For instance,encoder 1012 may be configured to encode data in accordance with various concepts and schemes of the present disclosure. Similarly,decoder 1014 may be configured to decode data in accordance with various concepts and schemes of the present disclosure.
• Processor 1060, as a special-purpose machine, may include non-generic and specially-designed hardware circuits that are designed, arranged and configured to perform specific tasks pertaining to QC-LDPC coding in accordance with various implementations of the present disclosure. In one aspect,processor 1060 may execute the one or more sets of codes, programs and/orinstructions 1072 stored inmemory 1070 to perform various operations to render power-save operations in accordance with various implementations of the present disclosure. In another aspect,processor 1060 may include anencoder 1062 and adecoder 1064 that performs specific tasks and functions to render QC-LDPC coding in accordance with various implementations of the present disclosure. For instance,encoder 1062 may be configured to encode data in accordance with various concepts and schemes of the present disclosure. Likewise,decoder 1064 may be configured to decode data in accordance with various concepts and schemes of the present disclosure.
• Each offirst apparatus 1005 andsecond apparatus 1050 may be configured to implement each ofprocesses 1100, 1200 and 1300 described below. Thus, to avoid redundancy and in the interest of brevity, operations offirst apparatus 1005 andsecond apparatus 1050, as well asprocessor 1010 andprocessor 1060, are described below in the context ofprocesses 1100, 1200 and 1300. It is noteworthy that, although the description below is provided in the context offirst apparatus 1005, the description below is also applicable tosecond apparatus 1050.
• FIG. 11 illustrates anexample process 1100 in accordance with an implementation of the present disclosure.Process 1100 may represent an aspect of implementing the proposed concepts and schemes such as those described with respect to some or all ofFIG. 1 - FIG. 9. More specifically,process 1100 may represent an aspect of the proposed concepts and schemes pertaining to multi-embedded LDPC code design and shift-coefficient design.Process 1100 may include one or more operations, actions, or functions as illustrated by one or more ofblocks 1110, 1120, 1130 and 1140. Although illustrated as discrete blocks, various blocks ofprocess 1100 may be divided into additional blocks, combined into fewer blocks, or eliminated, depending on the desired implementation. Moreover, the blocks/sub-blocks ofprocess 1100 may be executed in the order shown inFIG. 11 or, alternatively in a different order.Process 1100 may be implemented bycommunications system 1000 and any variations thereof. For instance,process 1100 may be implemented in or byfirst apparatus 1005 and/orsecond apparatus 1050. Solely for illustrative purposes and without limiting the scope,process 1100 is described below in the context offirst apparatus 1005.Process 1100 may begin atblock 1110.
• At 1110,process 1100 may involveprocessor 1010 offirst apparatus 1005 generating a QC-LDPC code having a plurality of codebooks embedded therein.Process 1100 may proceed from 1110 to 1120.
• At 1120,process 1100 may involveprocessor 1010 selecting a codebook from the plurality of codebooks.Process 1100 may proceed from 1120 to 1130.
• At 1130,process 1100 may involveprocessor 1010 encoding data using the selected codebook.Process 1100 may proceed from 1130 to 1140.
• At 1140,process 1100 may involveprocessor 1010 transmitting, viatransceiver 1030, the encoded data (e.g., to second apparatus 1050).
• In some implementations, each codebook of the plurality of codebooks may correspond to a respective hybrid automatic repeat request (HARQ) threads of a plurality of HARQ threads that are different from one another.
• In some implementations, in generating the QC-LDPC code having the plurality of codebooks embedded therein,process 1100 may involveprocessor 1010 generating the QC-LDPC code which includes a base matrix and a shift-coefficient matrix. The base matrix may include a parity matrix of a plurality of parity bits and an information matrix of a plurality of information bits. Each codebook of the plurality of codebooks may include the parity matrix and a respective portion of the information matrix of a corresponding size such that sizes of the plurality of codebooks are different from one another.
• In some implementations, each codebook of the plurality of codebooks may correspond to a respective design of a plurality of designs of the shift-coefficient matrix.
• In some implementations, in generating the QC-LDPC code having the plurality of codebooks embedded therein,process 1100 may involveprocessor 1010 generating a respective table of shift values for each lifting factor of a first set of lifting factors. Moreover,process 1100 may involveprocessor 1010 optimizing the first set of lifting factors to produce a second set of lifting factors. The number of lifting factors of the first set may be greater than a number of lifting factors of the second set. A first lifting factor that exists in the first set but not in the second set may share a respective table of shift values of a second lifting factor that exists in both the first set and the second set. The second lifting factor may be smaller than the first lifting factor in value and closest to the first lifting factor than other lifting factors in the first set.
• In some implementations, in selecting the codebook from the plurality of codebooks,process 1100 may involveprocessor 1010 selecting the codebook from the plurality of codebooks based on an initial code rate for transmission of the data, a code block size of the data, or both.
• In some implementations, in selecting the codebook from the plurality of codebooks,process 1100 may involveprocessor 1010 performing a number of operations (e.g., similar to those involved in logic flow 200). For instance,process 1100 may involveprocessor 1010 determining whether a code block size of the data is less than a threshold code block size. In response to the code block size of the data being less than the threshold code block size,process 1100 may involveprocessor 1010 selecting a third codebook of the plurality of codebooks. In response to the code block size of the data being not less than the threshold code block size,process 1100 may involveprocessor 1010 determining whether an initial code rate for transmission of the data is greater than a threshold code rate. In response to the initial code rate being not greater than the threshold code rate,process 1100 may involveprocessor 1010 selecting a second codebook of the plurality of codebooks. In response to the initial code rate being greater than the threshold code rate,process 1100 may involveprocessor 1010 selecting a first codebook of the plurality of codebooks. A size of the first codebook may be larger than a size of the second codebook. The size of the second codebook may be larger than a size of the third codebook.
• Alternatively or additionally, in selecting the codebook from the plurality of codebooks,process 1100 may involveprocessor 1010 performing a number of other operations. For instance,process 1100 may involveprocessor 1010 determining a code block size of the data. Based on a result of the determination,process 1100 may involveprocessor 1010 selecting a first codebook of the plurality of codebooks responsive to the code block size being determined to be greater than a first threshold code block size. Additionally,process 1100 may involveprocessor 1010 selecting a second codebook of the plurality of codebooks responsive to the code block size being determined to be greater than a second threshold code block size. Moreover,process 1100 may involveprocessor 1010 selecting a third codebook of the plurality of codebooks responsive to the code block size being determined to be greater than a third threshold code block size. The first threshold code block size may be greater than the second threshold code block size. The second threshold code block size may be greater than the third threshold code block size. A size of the first codebook may be larger than a size of the second codebook. The size of the second codebook may be larger than a size of the third codebook.
• FIG. 12 illustrates anexample process 1200 in accordance with an implementation of the present disclosure.Process 1200 may represent an aspect of implementing the proposed concepts and schemes such as those described with respect to some or all ofFIG. 1 - FIG. 9. More specifically,process 1200 may represent an aspect of the proposed concepts and schemes pertaining to hybrid orthogonal LDPC layer design and QC-LDPC support of extreme low code rate.Process 1200 may include one or more operations, actions, or functions as illustrated by one or more ofblocks 1210, 1220 and 1230. Although illustrated as discrete blocks, various blocks ofprocess 1200 may be divided into additional blocks, combined into fewer blocks, or eliminated, depending on the desired implementation. Moreover, the blocks/sub-blocks ofprocess 1200 may be executed in the order shown inFIG. 12 or, alternatively in a different order.Process 1200 may be implemented bycommunications system 1000 and any variations thereof. For instance,process 1200 may be implemented in or byfirst apparatus 1005 and/orsecond apparatus 1050. Solely for illustrative purposes and without limiting the scope,process 1200 is described below in the context offirst apparatus 1005.Process 1200 may begin atblock 1210.
• At 1210,process 1200 may involveprocessor 1010 offirst apparatus 1005 generating a QC-LDPC code that comprises at least one quasi-row orthogonal layer.Process 1200 may proceed from 1210 to 1220.
• At 1220,process 1200 may involveprocessor 1010 encoding data using the QC-LDPC code.Process 1200 may proceed from 1220 to 1230.
• At 1230,process 1200 may involveprocessor 1010 transmitting, viatransceiver 1030, the encoded data (e.g., to second apparatus 1050).
• In some implementations, the at least one quasi-row orthogonal layer may include a plurality of rows and a plurality of columns of bits. One or more columns of the plurality of columns of the at least one quasi-row orthogonal layer may include at least one punctured column of degree two or more. The remaining columns of the plurality of columns of the at least one quasi-row orthogonal layer may include non-punctured columns of degree one or zero.
• In some implementations, there may be no cycle within the punctured columns.
• In some implementations, the QC-LDPC code may include a hybrid orthogonality design having a plurality of portions of different degrees of orthogonality. A first portion of the plurality of portions of a low degree of orthogonality may correspond to a high code rate, and a second portion of the plurality of portions of a high degree of orthogonality may correspond to a low code rate.
• In some implementations, the plurality of portions of different degrees of orthogonality may include some or all of the following: (1) a non-row orthogonal portion comprising a plurality of rows and a plurality of columns forming at least one non-row orthogonal layer, (2) a quasi-row orthogonal portion comprising a plurality of rows and a plurality of columns forming the at least one quasi-row orthogonal layer, and (3) a pure-row orthogonal portion comprising a plurality of rows and a plurality of columns forming at least one pure-row orthogonal layer. The plurality of columns of the non-row orthogonal portion may include at least one punctured column of degree two or more as well as non-punctured columns of degree one or zero. One or more columns of the plurality of columns of the quasi-row orthogonal portion may include at least one punctured column of degree two or more. The remaining columns of the plurality of columns of the quasi-row orthogonal portion may include non-punctured columns of degree one or zero. Each column of the plurality of columns of the pure-row orthogonal portion may include a column of degree one or zero.
• In some implementations, the QC-LDPC code may include a parity matrix of a plurality of parity bits and an information matrix of a plurality of information bits. One or more rows of bits through the information matrix and the parity matrix may include one or more rows of bits each of degree two.
• In some implementations, each bit of bits of the degree two of the one or more rows of bits of degree two may include a previously-used parity bit or a previously-transmitted information bit.
• FIG. 13 illustrates anexample process 1300 in accordance with an implementation of the present disclosure.Process 1300 may represent an aspect of implementing the proposed concepts and schemes such as those described with respect to some or all ofFIG. 1 - FIG. 9. More specifically,process 1300 may represent an aspect of the proposed concepts and schemes pertaining to kernel matrix design.Process 1300 may include one or more operations, actions, or functions as illustrated by one or more ofblocks 1310, 1320 and 1330. Although illustrated as discrete blocks, various blocks ofprocess 1300 may be divided into additional blocks, combined into fewer blocks, or eliminated, depending on the desired implementation. Moreover, the blocks/sub-blocks ofprocess 1300 may be executed in the order shown inFIG. 13 or, alternatively in a different order.Process 1300 may be implemented bycommunications system 1000 and any variations thereof. For instance,process 1300 may be implemented in or byfirst apparatus 1005 and/orsecond apparatus 1050. Solely for illustrative purposes and without limiting the scope,process 1300 is described below in the context offirst apparatus 1005.Process 1300 may begin atblock 1310.
• At 1310,process 1300 may involveprocessor 1010 offirst apparatus 1005 generating a QC-LDPC code that including a base matrix a portion of which forming a kernel matrix that corresponds to a code rate of at least a threshold value.Process 1300 may proceed from 1310 to 1320.
• At 1320,process 1300 may involveprocessor 1010 encoding data using the QC-LDPC code.Process 1300 may proceed from 1320 to 1330.
• At 1330,process 1300 may involveprocessor 1010 transmitting, viatransceiver 1030, the encoded data (e.g., to second apparatus 1050).
• In some implementations, the code rate may be 0.89.
• In some implementations, the kernel matrix may include a plurality of rows and a plurality of columns of bits. Two or more of the columns may include punctured columns having a specific pattern of bits.
• In some implementations, the specific pattern of bits in the punctured columns may include one or more bits of 0 within the punctured columns after any number of column permutation(s) and/or row permutation(s) (e.g., at least one column permutation, at least one row permutation, or any combination thereof). Two examples of a specific pattern including one or more bits of 0 after column permutation(s) and/or row permutation(s) are shown in part (A) ofFIG. 7. In some implementations, the specific pattern of bits in the punctured columns may include an isosceles right triangle of bits of 0, with a right angle of the triangle corresponding to a bit of 0 at an upper-left corner of the punctured columns. An example of such an isosceles right triangle of bits of 0 is shown in part (B) ofFIG. 7.
• In some implementations, the kernel matrix may include a parity matrix of a plurality of rows and a plurality of columns of bits. The kernel matrix may also include an information matrix of a plurality of rows and a plurality of columns of bits. The parity matrix may include a matrix having a Wi-Fi pattern. More than one rows of bits of the information matrix excluding punctured columns of the kernel matrix may include rows of high density of bits of 1 with no or one bit of 0. The rows of high density bits may correspond to rows of the Wi-Fi pattern.
• In some implementations, a bottom row of bits of the plurality of rows may include a first number of bits of 1. The first number may be equal to or greater than a number of punctured columns by zero, one, two or three (e.g., by a few). In some implementations, a portion of the first number of bits of 1 in the bottom row may correspond to the punctured columns and a right-most column of the kernel matrix bordering a right side of the Wi-Fi pattern.
• In some implementations, the kernel matrix may include five rows of bits and twenty columns of bits. A variable node degree of the twenty columns of bits may include one of the following: [2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], [2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3], and [2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]. A check node degree of the five rows of bits may include one of the following: [13, 10, 14, 17, 2], [13, 10, 13, 17, 2], [13, 10, 13, 18, 3], [13, 11, 13, 18, 2], [13, 10, 14, 18, 2], [13, 10, 13, 19, 2], [14, 10, 13, 18, 1], [13, 11, 13, 18, 1], [13, 10, 14, 18, 1], [13, 11, 13, 19, 1], [13, 10, 13, 18, 2], and [13, 10, 13, 18, 1].
• FIG. 14 illustrates anexample process 1400 in accordance with an implementation of the present disclosure.Process 1400 may represent an aspect of implementing the proposed concepts and schemes such as those described with respect toFIG. 9. More specifically,process 1300 may represent an aspect of the proposed concepts and schemes pertaining to shift-coefficient design.Process 1400 may include one or more operations, actions, or functions as illustrated by one or more ofblocks 1410, 1420 and 1430 as well as sub-blocks 1412 and 1414. Although illustrated as discrete blocks, various blocks ofprocess 1400 may be divided into additional blocks, combined into fewer blocks, or eliminated, depending on the desired implementation. Moreover, the blocks/sub-blocks ofprocess 1400 may be executed in the order shown inFIG. 14 or, alternatively in a different order.Process 1400 may be implemented bycommunications system 1000 and any variations thereof. For instance,process 1400 may be implemented in or byfirst apparatus 1005 and/orsecond apparatus 1050. Solely for illustrative purposes and without limiting the scope,process 1400 is described below in the context offirst apparatus 1005.Process 1400 may begin atblock 1410.
• At 1410,process 1400 may involveprocessor 1010 offirst apparatus 1005 generating a QC-LDPC code.Process 1400 may proceed from 1410 to 1420.
• At 1420,process 1400 may involveprocessor 1010 encoding data using the QC-LDPC code.Process 1400 may proceed from 1420 to 1430.
• At 1430,process 1400 may involveprocessor 1010 transmitting, viatransceiver 1030, the encoded data (e.g., to second apparatus 1050).
• In generating the QC-LDPC code,process 1400 may involveprocessor 1010 performing a number of operations as represented by sub-blocks 1412 and 1414.
• At 1412,process 1400 may involveprocessor 1010 generating a respective table of shift values for each lifting factor of a first set of lifting factors.Process 1400 may proceed from 1412 to 1414.
• At 1414,process 1400 may involveprocessor 1010 optimizing the first set of lifting factors to produce a second set of lifting factors.
• A number of lifting factors of the first set may be greater than a number of lifting factors of the second set. A first lifting factor that exists in the first set but not in the second set may share a respective table of shift values of a second lifting factor that exists in both the first set and the second set. The second lifting factor may be smaller than the first lifting factor in value and closest to the first lifting factor than other lifting factors in the first set.
Additional Notes
• The herein-described subject matter sometimes illustrates different components contained within, or connected with, different other components. It is to be understood that such depicted architectures are merely examples, and that in fact many other architectures can be implemented which achieve the same functionality. In a conceptual sense, any arrangement of components to achieve the same functionality is effectively "associated" such that the desired functionality is achieved. Hence, any two components herein combined to achieve a particular functionality can be seen as "associated with" each other such that the desired functionality is achieved, irrespective of architectures or intermedial components. Likewise, any two components so associated can also be viewed as being "operably connected", or "operably coupled", to each other to achieve the desired functionality, and any two components capable of being so associated can also be viewed as being "operably couplable", to each other to achieve the desired functionality. Specific examples of operably couplable include but are not limited to physically mateable and/or physically interacting components and/or wirelessly interactable and/or wirelessly interacting components and/or logically interacting and/or logically interactable components.
• Further, with respect to the use of substantially any plural and/or singular terms herein, those having skill in the art can translate from the plural to the singular and/or from the singular to the plural as is appropriate to the context and/or application. The various singular/plural permutations may be expressly set forth herein for sake of clarity.
• Moreover, it will be understood by those skilled in the art that, in general, terms used herein, and especially in the appended claims, e.g., bodies of the appended claims, are generally intended as "open" terms, e.g., the term "including" should be interpreted as "including but not limited to," the term "having" should be interpreted as "having at least," the term "includes" should be interpreted as "includes but is not limited to," etc. It will be further understood by those within the art that if a specific number of an introduced claim recitation is intended, such an intent will be explicitly recited in the claim, and in the absence of such recitation no such intent is present. For example, as an aid to understanding, the following appended claims may contain usage of the introductory phrases "at least one" and "one or more" to introduce claim recitations. However, the use of such phrases should not be construed to imply that the introduction of a claim recitation by the indefinite articles "a" or "an" limits any particular claim containing such introduced claim recitation to implementations containing only one such recitation, even when the same claim includes the introductory phrases "one or more" or "at least one" and indefinite articles such as "a" or "an," e.g., "a" and/or "an" should be interpreted to mean "at least one" or "one or more;" the same holds true for the use of definite articles used to introduce claim recitations. In addition, even if a specific number of an introduced claim recitation is explicitly recited, those skilled in the art will recognize that such recitation should be interpreted to mean at least the recited number, e.g., the bare recitation of "two recitations," without other modifiers, means at least two recitations, or two or more recitations. Furthermore, in those instances where a convention analogous to "at least one of A, B, and C, etc." is used, in general such a construction is intended in the sense one having skill in the art would understand the convention, e.g., "a system having at least one of A, B, and C" would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc. In those instances where a convention analogous to "at least one of A, B, or C, etc." is used, in general such a construction is intended in the sense one having skill in the art would understand the convention, e.g., "a system having at least one of A, B, or C" would include but not be limited to systems that have A alone, B alone, C alone, A and B together, A and C together, B and C together, and/or A, B, and C together, etc. It will be further understood by those within the art that virtually any disjunctive word and/or phrase presenting two or more alternative terms, whether in the description, claims, or drawings, should be understood to contemplate the possibilities of including one of the terms, either of the terms, or both terms. For example, the phrase "A or B" will be understood to include the possibilities of "A" or "B" or "A and B."
• From the foregoing, it will be appreciated that various implementations of the present disclosure have been described herein for purposes of illustration, and that various modifications may be made without departing from the scope and spirit of the present disclosure. Accordingly, the various implementations disclosed herein are not intended to be limiting, with the true scope and spirit being indicated by the following claims.

Claims (13)

1. A method, comprising:

   generating, by a processor of an apparatus, a quasi-cyclic-low-density parity-check (QC-LDPC) code having a plurality of codebooks embedded therein;

   selecting, by the processor, a codebook from the plurality of codebooks; and

   encoding, by the processor, data using the selected codebook.
2. The method of Claim 1, wherein each codebook of the plurality of codebooks corresponds to a respective hybrid automatic repeat request (HARQ) threads of a plurality of HARQ threads that are different from one another.
3. The method of Claim 1, wherein the generating of the QC-LDPC code having the plurality of codebooks embedded therein comprises generating the QC-LDPC code that comprises a base matrix and a shift-coefficient matrix,
   wherein the base matrix comprises a parity matrix of a plurality of parity bits and an information matrix of a plurality of information bits, and
   wherein each codebook of the plurality of codebooks comprises the parity matrix and a respective portion of the information matrix of a corresponding size such that sizes of the plurality of codebooks are different from one another.
4. The method of Claim 3, wherein each codebook of the plurality of codebooks corresponds to a respective design of a plurality of designs of the shift-coefficient matrix.
5. The method of Claim 1, wherein the selecting of the codebook from the plurality of codebooks comprises selecting the codebook from the plurality of codebooks based on an initial code rate for transmission of the data, a code block size of the data, or both.
6. The method of Claim 1, wherein the selecting of the codebook from the plurality of codebooks comprises:

   determining whether a code block size of the data is less than a threshold code block size;

   responsive to the code block size of the data being less than the threshold code block size, selecting a third codebook of the plurality of codebooks;

   responsive to the code block size of the data being not less than the threshold code block size, determining whether an initial code rate for transmission of the data is greater than a threshold code rate;

   responsive to the initial code rate being not greater than the threshold code rate, selecting a second codebook of the plurality of codebooks; and

   responsive to the initial code rate being greater than the threshold code rate, selecting a first codebook of the plurality of codebooks,

   wherein a size of the first codebook is larger than a size of the second codebook,and

   wherein the size of the second codebook is larger than a size of the third codebook.
7. The method of Claim 1, wherein the selecting of the codebook from the plurality of codebooks comprises:

   determining a code block size of the data; and

   selecting the codebook by:

   selecting a first codebook of the plurality of codebooks responsive to the code block size being determined to be greater than a first threshold code block size;

   selecting a second codebook of the plurality of codebooks responsive to the code block size being determined to be greater than a second threshold code block size; and

   selecting a third codebook of the plurality of codebooks responsive to the code block size being determined to be greater than a third threshold code block size,

   wherein the first threshold code block size is greater than the second threshold code block size,

   wherein the second threshold code block size is greater than the third threshold code block size,

   wherein a size of the first codebook is larger than a size of the second codebook,and

   wherein the size of the second codebook is larger than a size of the third codebook.
8. A method, comprising:

   generating, by a processor of an apparatus, a quasi-cyclic-low-density parity-check (QC-LDPC) code that comprises at least one quasi-row orthogonal layer; and

   encoding, by the processor, data using the QC-LDPC code.
9. The method of Claim 8, wherein the at least one quasi-row orthogonal layer comprises a plurality of rows and a plurality of columns of bits, wherein one or more columns of the plurality of columns of the at least one quasi-row orthogonal layer comprise at least one punctured column of degree two or more, and wherein remaining columns of the plurality of columns of the at least one quasi-row orthogonal layer comprise non-punctured columns of degree one or zero.
10. The method of Claim 9, wherein there is no cycle within the punctured columns.
11. The method of Claim 8, wherein the QC-LDPC code comprises a hybrid orthogonality design comprising a plurality of portions of different degrees of orthogonality, wherein a first portion of the plurality of portions of a low degree of orthogonality corresponds to a high code rate, and wherein a second portion of the plurality of portions of a high degree of orthogonality corresponds to a low code rate.
12. The method of Claim 11, wherein the plurality of portions of different degrees of orthogonality comprise:

    a non-row orthogonal portion comprising a plurality of rows and a plurality of columns forming at least one non-row orthogonal layer;

    a quasi-row orthogonal portion comprising a plurality of rows and a plurality of columns forming the at least one quasi-row orthogonal layer; and

    a pure-row orthogonal portion comprising a plurality of rows and a plurality of columns forming at least one pure-row orthogonal layer,

    wherein the plurality of columns of the non-row orthogonal portion comprises at least one punctured column of degree two or more and non-punctured columns of degree one or zero,

    wherein one or more columns of the plurality of columns of the quasi-row orthogonal portion comprise at least one punctured column of degree two or more,

    wherein remaining columns of the plurality of columns of the quasi-row orthogonal portion comprise non-punctured columns of degree one or zero, and

    wherein each column of the plurality of columns of the pure-row orthogonal portion comprises a column of degree one or zero.
13. The method of Claim 8, wherein the QC-LDPC code comprises a parity matrix of a plurality of parity bits and an information matrix of a plurality of information bits, and wherein one or more rows of bits through the information matrix and the parity matrix comprises one or more rows of bits each of degree two.

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